Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps into deep learning's abilities to uncover parameters governing intricate behaviors in nonlinear equations. We validate our approach using synthetic data and predefined functions that model system dynamics. By training the neural network with noisy time series data, it fine-tunes the Huber loss function to converge to accurate parameters. We apply our method to damped oscillators, Van der Pol oscillators, Lotka-Volterra systems, and Lorenz systems under multiplicative noise. The trained neural network accurately estimates parameters, evident from closely matching latent dynamics. Comparing true and estimated trajectories visually reinforces our method's precision and robustness. Our study underscores the Huber loss-guided neural network as a versatile tool for parameter estimation, effectively uncovering complex relationships in nonlinear systems. The method navigates noise and uncertainty adeptly, showcasing its adaptability to real-world challenges.

翻译：在复杂非线性系统中精确估计参数对于科学和工程领域至关重要。我们提出了一种基于Huber损失函数的神经网络参数估计新方法。该方法利用深度学习的能力，揭示非线性方程中支配复杂行为的潜在参数。我们通过合成数据和预定义的系统动力学模型函数验证了该方法的有效性。通过使用含噪声的时间序列数据训练神经网络，该方法能优化Huber损失函数，从而收敛到精确的参数值。我们将该方法应用于乘性噪声下的阻尼振荡器、范德波尔振荡器、Lotka-Volterra系统和Lorenz系统。训练后的神经网络能够准确估计参数，其潜在动力学行为的精确匹配证实了这一点。通过对比真实轨迹与估计轨迹的可视化分析，进一步佐证了该方法的精度与鲁棒性。本研究揭示了基于Huber损失函数的神经网络作为参数估计通用工具的有效性，能够有效挖掘非线性系统中的复杂关联。该方法能够灵活应对噪声和不确定性，展现了其在真实世界挑战中的适应性。